Faculty Publications
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Item In this paper we consider a two parameter family of two-step methods for the accurate numerical integration of second order periodic initial value problems. By applying the methods to the test equation y? + ?2y = 0, we determine the parameters ?, ? so that the phase-lag (frequency distortion) of the method is minimal. The resulting method is a P-stable method with a minimal phase-lag ?6h6/42000. The superiority of the method over the other P-stable methods is illustrated by a comparative study of the phase-lag errors and by illustrating with a numerical example. © 1986.(A class of two-step P-stable methods for the accurate integration of second order periodic initial value problems) Ananthakrishnaiah, U.1986Item In this paper E-stable methods of O(h4), O(h8) and O(h12) are derived for the direct numerical integration of initial value problems of second order differential equations with exponentially decreasing solutions. Numerical results are presented for both linear and nonlinear problems. © 1985 BIT Foundations.(Kluwer Academic Publishers, E-stable methods for exponentially decreasing solutions of second order initial value problems) Ananthakrishnaiah, U.1985